This lively (and at times emotional) presentation will feature a history of the solution of algebraic equations and conclude with a discussion of the life and times of composer Hector Berlioz and mathematician Evariste Galois in post-Napoleonic France.
It will be accessible to anyone who understands the quadratic formula.
A day in the life of an actuaryActuaries analyze risk, forecasting an organization’s potential for loss (or profit), playing a key role in helping organizations plan the future. We use mathematical models to assist in solving complex problems. Today, I will provide a brief overview of my background and current role. Then I will review three “areas” of mathematics that are used during a typical actuary's career. I will provide an example of how loss distributions (the third area) are used to model potential insurance claims. We will explore how these models can be used to determine the potential for losses of different sizes.
Linear Regression is a commonly used tool in modeling problems but is rarely understood by its users. A vector calculus approach of this topic will be explored to give a geometric interpretation of the ideas behind the regression line, the correlation coefficient, and what is meant by the term “least squares”. An extension to quadratic, cubic, and planar regression will also be developed using basic linear algebra.
In this talk, contingency tables that display relationships between categorical variables are introduced. To describe a contingency table I define some primary parameters. Also two statistical methods for analyzing contingency tables are presented, namely, independence test and estimation of cell probabilities. These two methods play a vital role in categorical data analysis, and both assume a Multinomial sampling. Lastly I focus on model building for two-way contingency tables, which is connected to the research for my Ph. D. dissertation.
Regression analysis is a statistical methodology that utilizes the relationship between two or more quantitative variables. The aim of this talk is intuitively to investigate three methods in building linear regression: Least Squares, Maximum Likelihood and Nonparametric. We will discuss the geometry behind these methods.
This Small Business Innovation Research (SBIR) Phase I project develops a mathematically engineered DNA-based covert taggant security technology, called ComDBarTag, that forensically marks objects with synthetic DNA nano-barcodes for brand protection, product liability protection, verification of authenticity and forensic track and trace-back. Pharmaceutical manufacturers, petrochemical companies, brand owners and governments need thousands of covert and unique signatures to protect their drugs, fuel, products, documents and citizens.
The broader impacts of this research include anti-counterfeiting, law enforcement, liability protection, and improved public health and safety. Counterfeiting costs the U.S. economy $250 billion per year and is responsible for the loss of 750,000 American jobs. The counterfeiting of the drug heparin has been linked to the deaths of over a hundred Americans with hundreds more having severe allergic reactions. Counterfeit fuel causes losses of about $100 billion per year worldwide to governments and private enterprises due to adulteration, theft, diversion and excise tax evasion. Adulterated gasoline damages automotive components and its combustion harms public health.
Applications of some mathematical methods will also be discussion.